Variable Refractive Index

Q. A light beam is travelling from Region I to Region IV (refer figure). The refractive index in Region I, II, III and IV are $n_0,\frac{n_0}{2},\frac{n_0}{6}and\frac{n_0}{8}$ respectively. The angle of incidence $\theta$ for which the beam just misses entering Region IV is

(IIT-JEE 2008)

1. $si{n}^{-1}\left(\frac{3}{4}\right)$
2. $si{n}^{-1}\left(\frac{1}{8}\right)$
3. $si{n}^{-1}\left(\frac{1}{4}\right)$
4. $si{n}^{-1}\left(\frac{1}{3}\right)$

Q. A system of coordinates is drawn in a medium whose refractive index varies as $\mu =\frac{2}{1+y^2}$, where $0\le y\le 1$ and $\mu =2$ for $y<0$ as shown in figure. A ray of light is incident at origin at an angle ${60}^{\circ }$ with y - axis as shown in the figure. At point $P$, ray becomes parallel to x - axis. The value of $H$ is:-

1. ${(\frac{2}{\sqrt{3}}-1)}^{\frac{1}{2}}$
2. ${\left(\frac{2}{\sqrt{3}}\right)}^{\frac{1}{2}}$
3. ${(\sqrt{3}-1)}^{\frac{1}{2}}$
4. ${(\frac{4}{\sqrt{3}}-1)}^{\frac{1}{2}}$

Q.

A ray light is incident at the glass-water interface at an angle i, it merges finally parallel to the surface of water, then the value of ${\mu }_g$ would be

1. (4/3) sin i

2. 1 /sin i

3. 4/3

4. 1

Q. An air bubble inside a water tank would behave as a

1. Concave lens
2. Convex lens
3. May be both
4. Neither concave, nor convex lens